9,006 research outputs found
Study of Algorithms for Fast Computation of Crack Expansion Problem
International audienceA problem of quasi-static growth of an arbitrary shaped-crack along an interface requires many times of iterations not only for finding a spatial distribution of discontinuity but also for determining the crack tip. This is crucial when refining model resolution and also when the phenomena progresses quickly from one step to another. We propose a mathematical reformu-lation of the problem as a nonlinear equation and adopt different numerical methods to solve it efficiently. Compared to a previous work of the authors, the resulting code shows a great improvement of performance. This gain is important for further application of aseismic slip process along the fault interface, in the context of plate convergence as well as the reactivation of fault systems in reservoirs
Fast shape reconstruction of perfectly conducting cracks by using a multi-frequency topological derivative strategy
This paper concerns a fast, one-step iterative technique of imaging extended
perfectly conducting cracks with Dirichlet boundary condition. In order to
reconstruct the shape of cracks from scattered field data measured at the
boundary, we introduce a topological derivative-based electromagnetic imaging
function operated at several nonzero frequencies. The properties of the imaging
function are carefully analyzed for the configurations of both symmetric and
non-symmetric incident field directions. This analysis explains why the
application of incident fields with symmetric direction operated at multiple
frequencies guarantees a successful reconstruction. Various numerical
simulations with noise-corrupted data are conducted to assess the performance,
effectiveness, robustness, and limitations of the proposed technique.Comment: 17 pages, 27 figure
Numerical study of geometrical dispersion in self-affine rough fractures
We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-affine surfaces rigidly translated with respect to each other. Geometrical dispersion due to the disorder of the velocity distribution is computed using the lubrication approximation. Using a spectral perturbative scheme to solve the flow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulations to test theoretical predictions on the dispersion dependence on simple geometrical parameters. We observe the expected quadratic dispersion coefficient dependence on both the mean aperture and the relative shift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-affine curve whose exponent is equal to that of the fracture surface
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
A Dynamic Atomistic-Continuum Method for the Simulation of Crystalline Materials
We present a coupled atomistic-continuum method for the modeling of defects
and interface dynamics of crystalline materials. The method uses atomistic
models such as molecular dynamics near defects and interfaces, and continuum
models away from defects and interfaces. We propose a new class of matching
conditions between the atomistic and continuum regions. These conditions ensure
the accurate passage of large scale information between the atomistic and
continuum regions and at the same time minimize the reflection of phonons at
the atomistic-continuum interface. They can be made adaptive if we choose
appropriate weight functions. We present applications to dislocation dynamics,
friction between two-dimensional crystal surfaces and fracture dynamics. We
compare results of the coupled method and the detailed atomistic model.Comment: 48 pages, 20 figure
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